Question

derivative of tan^2x+sinx

Answer 1

i rewrote the function as (tanx)^2+sinx

Answer 2

=tan(x)tan(x) + sin(x)
you need to use the product rule on the first part, and the second part is simple derivation
so let u=tan(x) v=tan(x)
so the derivative of tan(^2)x will be
uv'+vu'
then add the derivative of sin(x) on the end

does that make sense?
if you struggle to differentiate tan(x), think of it as sinx/cosx and use the quotient rule

Answer 3

okay so i have f'(x)= 2tanxsec^2x+cosx

Answer 4

yep that's correct! :)

Answer 5

the question asks me to do f'(pi/4) how can i plug that in?

Answer 6

okay so if you know f '(x) ie what you've just worked out, simply replace all of your x's by pi/4 and you'll get your answer!

Answer 7

yes but how can i plug it in into sec^2x? my calculator doesnt let me do that

Answer 8

oh okay i see what you mean. you can just do 1/[(cos x)*cos(x)]

Answer 9

ooh okay got it thank you:)

Answer 10

you're welcome! good work :)